The field equation (REF ) cannot give a meaningful field equation at \(n=4\) . However, Glavan & Lin D. Glavan and Lin [1]} shown that by a re-scaling \(\alpha \rightarrow \alpha / (n-4)\)  and Ghosh & Maharaj [2]} by considering spacetimes of curvature scale \(\mathcal {K}\)  which are maximally symmetric determined the variation of the Gauss-Bonnet contribution as
\({1 \over \sqrt{-g}}~g_{\mu \lambda }~{\delta \mathcal {L}_{GB} \over \delta g_{\nu \lambda }}={\alpha (n-2)(n-3) \over 2(n-1)}~\mathcal {K}^2~\delta ^\nu _\mu \) 
